Laplace transform

The Laplace transform of a function f(t) defined for all real numbers t ≥ 0 is the function F(s), defined by:

F(s) = ∫₀^∞ e^-st f(t) dt

The Laplace transform F(s) typically exists for all real numbers s > a, where a is a constant which depends on the growth behavior of f(t).

The Laplace transform is named after its discoverer Pierre-Simon Laplace.

See also: Fourier transform, transfer function, linear dynamic system.